Much understanding has been derived from the Eigenstate Thermalization Hypothesis [1]}, [2]} and it has become clear that entanglement is an important ingredient in thermalization, yet the latter is barely explored for gauge theories because of its ambiguous definition [3]}, [4]}, [5]}, [6]}. In this work, we overcome this issue for \(\mathbf {Z}_2\)  LGT in (2+1) spacetime dimensions (\(\mathbf {Z}_2^{2+1}\) ), by developing dual formulations `with entanglement cuts', allowing us to compute the Entanglement Structure of non-equilibrium states. Focusing on quench dynamics of an initial unentangled state, we investigate the `Entanglement Spectrum' (ES), a representation of a state in terms of an `Entanglement Hamiltonian' (EH), analogous to energy levels, first suggested by Li and Haldane as an indicator of topological order in non-Abelian fractional Quantum Hall effect systems [7]}.
